The super-Cotton tensor is naturally encoded in the action for conformal
supergravity,For the \(1\le {\cal N}\le 6\)  cases,
the complete nonlinear actions for \({\cal N}\) -extended conformal supergravity were
derived in [1]}, [2]} using the off-shell formulation for
\({\cal N}\) -extended conformal supergravity developed in [3]}.
The \({\cal N}=1\)  and \({\cal N}=2\)  conformal supergravity theories were constructed for the first time by van Nieuwenhuizen [4]}, and by
Roček and van Nieuwenhuizen [5]}, respectively.
The off-shell action for
\({\cal N}=6\)  conformal supergravity was independently derived by
Nishimura and Tanii [6]}.
On-shell formulations for \({\cal N}\) -extended conformal supergravity with \({\cal N}>2\) 
were given in [7]}, [8]}.
\(S_{\rm CSG}\) , in the following sense
[3]}, [2]}:
\({\cal W}\propto \frac{\delta S_{\rm CSG}}{\delta H}~.\) 
